A third bank, BNP Paribas, was kept on review for a possible downgrade.

German Chancellor Angela Merkel, French President Nicolas Sarkozy, and Greek Prime Minister George Papandreou later moved to ease market concerns over Greece by saying it was an "integral" member of the eurozone.

Meanwhile, the European Commission president, Jose Manuel Barroso, said he would put forward a proposal for the 17 eurozone governments to jointly guarantee their debts, via so-called eurobonds.

Stressed markets

Moody's said it was also planning to extend its review of all three banks "to consider the implications of the persistent fragility in the bank financing markets, given the banks' continued reliance on wholesale funding".

This further review could result in an additional one-notch downgrade, the agency warned.

The markets for short-term cash lending between European banks have become increasingly stressed in recent days, while share prices in European banks have fallen sharply.

Credit Agricole and Societe Generale have seen their share prices fall by about two-thirds since February, while BNP has fallen by more than half.

By late Monday afternoon trading, shares in Societe Generale had dropped a further 10%, eventually recovering some losses to end down 2.9%.

BNP Paribas finished 3.9% lower, while Credit Agricole rose 1.2%.

Both BNP Paribas and Societe Generale have issued statements in recent days to clarify the extent of their exposure to Greece and other troubled eurozone economies.

Moody's backed the two banks, saying they both had enough capital to provide "an adequate cushion to support its Greek, Portuguese and Irish exposures".

Fairly or not, these banks have been viewed as indulging in more creative accounting than other banks

SocGen has a total exposure to Greek government and commercial debts equal to 6.6bn euros, and BNP Paribas has 8.5bn euros, according to their disclosures to the European Banking Authority - both much lower than Credit Agricole's total of 27bn euros.

Nonetheless, Moody's still decided to downgrade Societe Generale, as it felt the bank no longer benefited from a higher level of French government support than its two rivals.

'Small downgrade'

All three banks' ratings have been on review since 15 June, and Moody's decision had been widely anticipated by the markets.

French central bank head Christian Noyer welcomed the downgrade decision as "relatively good news".

"French banks have an excellent rating, the same level as other major European banks - HSBC, Barclays, Deutsche Bank, Credit Suisse," he said.

"It's a very small downgrade, and Moody's had a higher rating than the other agencies so it's just put them on the same level or slightly better than the others."

However, the downgrade is likely to put further pressure on the banks, as many investors limit how much they are willing to lend to them or invest in their shares based on their credit ratings.

Meanwhile, the European Central Bank confirmed that two unnamed eurozone banks have asked for it to provide $575m of short-term dollar loans - the first time the emergency facility has been used since 17 August.